System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2

Average Error: 0.1 → 0.1

Time: 19.2s

Precision: 64

Math

\[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]

↓

\[\left(y \cdot \log z + \left(1 - z\right) \cdot y\right) + x \cdot 0.5\]

C

double f(double x, double y, double z) {
        double r12498504 = x;
        double r12498505 = 0.5;
        double r12498506 = r12498504 * r12498505;
        double r12498507 = y;
        double r12498508 = 1.0;
        double r12498509 = z;
        double r12498510 = r12498508 - r12498509;
        double r12498511 = log(r12498509);
        double r12498512 = r12498510 + r12498511;
        double r12498513 = r12498507 * r12498512;
        double r12498514 = r12498506 + r12498513;
        return r12498514;
}

↓

double f(double x, double y, double z) {
        double r12498515 = y;
        double r12498516 = z;
        double r12498517 = log(r12498516);
        double r12498518 = r12498515 * r12498517;
        double r12498519 = 1.0;
        double r12498520 = r12498519 - r12498516;
        double r12498521 = r12498520 * r12498515;
        double r12498522 = r12498518 + r12498521;
        double r12498523 = x;
        double r12498524 = 0.5;
        double r12498525 = r12498523 * r12498524;
        double r12498526 = r12498522 + r12498525;
        return r12498526;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.1
Target	0.1
Herbie	0.1

\[\left(y + 0.5 \cdot x\right) - y \cdot \left(z - \log z\right)\]

Derivation

1. Initial program 0.1

   \[x \cdot 0.5 + y \cdot \left(\left(1 - z\right) + \log z\right)\]
2. Using strategy rm

3. Applied distribute-rgt-in 0.1

   \[\leadsto x \cdot 0.5 + \color{blue}{\left(\left(1 - z\right) \cdot y + \log z \cdot y\right)}\]

4. Final simplification 0.1

   \[\leadsto \left(y \cdot \log z + \left(1 - z\right) \cdot y\right) + x \cdot 0.5\]

Reproduce

herbie shell --seed 2019169 
(FPCore (x y z)
  :name "System.Random.MWC.Distributions:gamma from mwc-random-0.13.3.2"

  :herbie-target
  (- (+ y (* 0.5 x)) (* y (- z (log z))))

  (+ (* x 0.5) (* y (+ (- 1.0 z) (log z)))))